Discover Mathematics P4: Term 1, Unit 4, Lessons 1–5
GoalFind the perimeter of rectangles, squares and other polygons.
New words
perimeter · the distance all the way around a shapelength (l) and width (w) · the two different sides of a rectanglepolygon · a closed shape with straight sides
Explanation
The perimeter of a shape is the length of its edge, as if you walked all the way around it once. To find it, add the lengths of all the sides. A rectangle has two lengths and two widths, so P = l + w + l + w = 2 × (l + w). For a rectangle 8 m long and 5 m wide, P = 2 × (8 + 5) = 2 × 13 = 26 m. A square has four equal sides, so P = 4 × side. A square with a side of 6 cm has P = 4 × 6 = 24 cm. For a polygon with different sides, add every side. Perimeter is a length, so it is measured in cm, m or km, and we must write the unit.
Worked examples
A rectangular garden is 8 m long and 5 m wide. P = 2 × (8 + 5) = 26 m. Check by adding the four sides: 8 + 5 + 8 + 5 = 26 m. Sherif needs 26 m of fence.
A square tile has a side of 6 cm. Its perimeter is 4 × 6 = 24 cm.
A five-sided plot has sides of 4 m, 6 m, 3 m, 5 m and 7 m. Add all the sides: 4 + 6 + 3 + 5 + 7 = 25 m.
Class activity
Walk the edge. Choose a room or a table at home. Measure its length and width with a tape or with steps. Work out the perimeter with the formula 2 × (l + w), and then check by adding the four sides. Are the two answers equal?
Practice
1
Find the perimeter of a rectangle 12 m long and 7 m wide.
2 × (12 + 7) = 2 × 19 = 38 m.
2
Find the perimeter of a square with a side of 15 cm.
4 × 15 = 60 cm.
3
A running track is a rectangle 90 m by 60 m. Mariam runs round it once. How far does she run?
2 × (90 + 60) = 2 × 150 = 300 m.
4
A triangle has sides of 9 cm, 12 cm and 15 cm. What is its perimeter?
9 + 12 + 15 = 36 cm.
5
Omar says the perimeter of a rectangle 10 cm by 4 cm is 40 cm because 10 × 4 = 40. What did he find instead?
He found the area (40 square cm). The perimeter is 2 × (10 + 4) = 28 cm.
